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zepelin [54]
2 years ago
12

How many students play all three sports: tennis, football and baseball?

Mathematics
1 answer:
alekssr [168]2 years ago
3 0

Answer:

6

Step-by-step explanation:

6 students play all three sports.

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The top of a 15-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 4 ft/sec.
Andrej [43]
The ladder, the ground and the wall form a right triangle; the ladder length (L) is the longest side of this triangle.  L^2 = h^2 + x^2, where h represents the height of the point on the wall where the ladder touches the wall, and x represents the distance of the base of the ladder from the wall.

We need dh/dt, which will be negative because the top of the ladder is sliding down the wall.

Starting with h^2 + x^2 = L^2, we differentiate (and subst. known values such as x = 5 feet and 4 ft/sec to find dh/dt.  Note that since the ladder length does not change, dL/dt = 0.  This leaves us with

      dh          dx
2h ---- + 2x ----- = 0.
       dt           dt

Since x^2 + h^2 = 15^2 = 225,          h^2 = 225 - (5 ft)^2 = 200, or
200 ft^2 = h^2.  Then h = + sqrt(200 ft^2) 

Substituting this into the differential equation, above:

2[sqrt(200)] (dh/dt) + 2 (5) (4 ft/sec) = 0.  Solve this for the desired quantity, dh/dt:

[sqrt(200)] (dh/dt) + (5)(4) = 0, or

                   dh/dt = -20 / sqrt(200) = (-1.41 ft / sec)   (answer)

This result is negative because the top of the ladder is moving downward.


4 0
3 years ago
PLEASE HELP!!! Write the expression as a single logarithm.<br> 3 log(4) + log(7)
anygoal [31]

Answer:

log (448)

Step-by-step explanation:

3 log(4) + log(7)

We know that a log b = log b^a

3 log(4) + log(7)

log 4^3 + log 7

log 64 + log 7

We know that log a + log b = log (a*b)

log (64 *7)

log (448)

3 0
3 years ago
Read 2 more answers
Two savings accounts were each opened with a $6,000 deposit. Account A earns compound interest at a 2% annual interest rate comp
Gnom [1K]

Answer:

Account A will earn approximately $7 more in interest than account B.

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Help me please?/+854​
eduard

Answer:

c

Step-by-step explanation:

if you look at the angle split it in half between the two intersections. the flip one of them over.

5 0
3 years ago
4) Find the m&lt;5, m&lt;7, and the m&lt;6 in the diagram below.
bazaltina [42]

Answer:

45,12,11

Step-by-step explanation:

voa respectively

8 0
2 years ago
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